aX+b (Edexcel International A Level (IAL) Maths): Revision Note

Dan Finlay

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aX+b

  • If a and b are constants then the following results are true

    • E(aX + b) = aE(X) + b

    • Var(aX + b) = a² Var(X)

  • Note that the mean is affected by multiplication and addition whereas addition does not change the variance

  • The factor of   includes the squared because the values of X are squared in the calculation

    • You could try and use the first result and the formula for variance to verify the second result

  • Remember a subtraction can be written as an addition

    • X – b can be written as X + (-b)

  • And division can be written as a multiplication

    • begin mathsize 16px style x over a end stylecan be written as begin mathsize 16px style 1 over a X end style

Worked Example

X is a random variable such that E left parenthesis X right parenthesis equals 5 and Var left parenthesis X right parenthesis equals 4.

Find the value of:

(i) straight E left parenthesis 3 X plus 5 right parenthesis

(ii) Var left parenthesis 3 X plus 5 right parenthesis

(iii) Var left parenthesis 2 minus X right parenthesis

2-2-1-ax--b-we-solution-1
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Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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